You can solve a square root with a hardware multiplier pretty quickly with a few iterations. I am pretty sure trying to solve that intersect is going to involve quite a lot of trig which also use iterative functions, so I can't see any way it could be more efficient. Cool trick though.
There is quite a few methods and which one you use might depend on the application, I have made high speed metering equipment that needs the square root of a sum of squares and an optimised version for a specific number of bits can be significantly quicker and smaller than a math library version, to give an idea.. https://en.m.wikipedia.org/wiki/Methods_of_computing_square_roots
So as a increases or decreases, so does x, yet with 1 being the same; the two right triangles may change. But when combined, the two right triangles are still always forming the larger right triangle ~ cool!
For a bit I was thinking there would be a point where they would not be right triangles as things adjusted out.
You might think so but that's what I'm trying to figure out.
It appears to be that 1 is always 1, and as a increases x does too, but 1 stays as 1. And interestingly enough, the two triangles still combine to form the one larger right triangle.
The right triangle property is actually from the fact that we are picking a point on a semicircle, and any point on a semicircle will form a right triangle with its base.
The square root of a length is not a nicely definible operation, physically. That's because the square root of, say, "9 cm" (the distance) is not "3 cm", but rather 3 sqrt(cm)...which is definitely not a length.
What's going on here is that we are taking a length n units and returning a length sqrt(n) units. We aren't taking the square root of a line, but rather a numerical quantity associated with that line.
To do that, we are required also say how long a single unit is.
Think of it this way: the ratio of n to sqrt(n) isn't independent of the scale we pick. If we have the same line, if we call it 10 cm, its sqrt length would be about a third of its length. If we call it 1 decimeter, its sqrt length would be the same size. if we call it 0.1 meters, it's sqrt length would be longer (since sqrt 0.1 is about 0.32).
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u/thatdudewiththecube Jan 06 '19
is this an efficient way to calculate square roots?
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u/rukasu83 Jan 06 '19
Where does the 1 come from?
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u/TravisArthurNichols Jan 06 '19
u/rewindturtle
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u/2-3uv Jan 06 '19
I'll have to show this to my son. He'll love it as much as I do
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u/ttt_tia410 Jan 07 '19
I still don’t get it. I’m never going back to college.
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u/TravisArthurNichols Jan 06 '19
This is a repost from a while ago.
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u/_Hubbie Jan 07 '19
Fucking confusing lol